S-parameters
MUSE
Material developed by Prof. L. Dunleavy, USF
© University of South Florida
1
2-Port Parameters
z
Recall Z-Parameters:
V
1
V
2
Z I Z I
11 1
12 2
Z I Z I
21 1
22 2
ª V1 º
!« »
¬ V2 ¼
I1
V1
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ªZ 11
«Z
¬ 21
Z 12 º ª I1 º
Z 22 »¼ «¬ I 2 »¼
I2
2-port
V2
2
2-Port Parameters
z
Recall Z-Parameters:
V
1
V
2
Z I Z I
11 1
12 2
Z I Z I
21 1
22 2
ª V1 º
!« »
¬ V2 ¼
I1
V1
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2-port
network
ªZ 11
«Z
¬ 21
Z 12 º ª I1 º
Z 22 »¼ «¬ I 2 »¼
I2
V2
3
2-PORT Parameters (cont’d)
z
Y-Parameters:
I1
I2
z
Y11V1 Y12 V2
Y21V1 Y22 V2
ª I1 º
!« »
¬I 2 ¼
ª Y11
«
¬Y21
Y12 º ª V1 º
»« »
Y22 ¼ ¬ V2 ¼
h-Parameters:
V1 h11I1 h12 V2
I 2 h 21I1 h 22 V2
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ª V1 º
!« »
¬ I2 ¼
ª h11
«h
¬ 21
h12 º ª I1 º
h 22 »¼ «¬ V2 »¼
4
2-Port Parameters (cont’d)
z
2-port Parameter Determination:
h 11
v1
I1
|v
2
0
I2
h21
|V 0
I1 2
V
1|
h
12 V I 0
2 1
I
h22 2 |I 0
V 1
2
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(Put a Short Circuit at Port #2)
(Put an Open Circuit at Port # 1)
5
S-Parameters
At high RF and Microwave frequencies direct
measurement of Y- , Z-, or H- parameters is
difficult due to:
• Unavailability of equipment to measure
RF/MW total current and voltage.
• Difficulty of obtaining perfect opens/shorts
• Active devices may be unstable under
open/short conditions.
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6
S-Parameters
For a two-port device there are four Sparameters S11, S21, S12, and S22
z S11, and S22 are simply the forward and
reverse reflection coefficients, with the
opposite port terminated in Z0 (usually 50
ohms.)
z S21 and S12 are simply the forward and
reverse gains assuming a Z0 source and load
(again usually 50 ohms).
z
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7
S-Parameters (cont’d)
z
S-Parameters:
b
S a s a
1
11 1 12 2
b
S a S a
2
21 1
22 2
a1
b1
ªb1 º
!« »
¬b 2 ¼
b2
ªS 11
«S
¬ 21
S 12 º ª a 1 º
S 22 »¼ «¬a 2 »¼
a2
2-port
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8
S-Parameters (cont’d)
z
Q. So what’s the deal with the a’s and b’s?
a1
b1
b2
a2
Zs
Vg
z
V1
2-port
V2
ZL
A. a1 and a2 are incident waves; b1 and b2 are
reflected waves
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9
Incident & Reflected Waves:
Simplified Case: Z1=Zs=Z2=ZL=Zo (real)
a1
a2
V1 Z 0 I 1
Incident port 1 voltage
E i1
2 Z0
Z0
Z0
V2 Z 0 I 2
2 Z0
Incident port 2 voltage
E i2
b1
b2
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Z0
Z0
V1 Z 0 I 1
reflected port 1 voltage
E r1
2 Z0
Z0
Z0
V2 Z 0 I 2
reflected port 2 voltage
2 Z0
Z0
E r2
Z0
10
S-Parameter Determination
s11
b1
|
a 1 a2
0
s21
b2
|
a1 a2 0
s12
b1
|
a2 a1 0
s22
b2
|
a2 a1 0
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= Input reflection coefficient *in
for case of ZL=Z0
= Forward transmission (insertion) gain
for case of ZL=Z0
= Reverse transmission (insertion) gain
for case of Zs=Z0
= Output reflection coefficient *out
for case of Zs=Z0
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Desired Measurement Conditions
Zs = Z0
a1
b1
Vg
b2
Z0
2-port
Z0
a2 = 0
V2
ZL =
Z0
Note…the input and output are terminated in Z0
a1
b1
Zs = Z0
Vg
Z0
*
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1-port
S11=*
12
GRAPHICAL VIEW OF SPARAMETERS
S12
S11,
Input
Refl.
Coeff. *in,
Return
Loss,
VSWR
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Reverse Gain
Insertion Loss,
Transmission Phase
Device
Under Test
S21, Forward Gain
Insertion Loss,
Transmission Phase
S22,
Output
Refl.
Coeff. *out,
Return
Loss,
VSWR
13
S-Parameters in Decibels
dB
Meaning or interpretation
S11
20 log10 |S11| Corresponds to the algebraic negative of the input
S12
20 log10 |S12| Reverse isolation (active device or amplifier), or
S21
20 log10 |S21| Power gain (active device or amplifier), or algebraic
S22
20 log10 |S22| Corresponds to the algebraic negative of the
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return loss of a 2-port with an R0 termination on
the opposite port.
algebraic negative of the insertion loss (I.L.) for a
passive device, with R0 at ports 1 and 2.
negative of the insertion loss (I.L.) for a passive
device, under matched R0 at ports 1 and 2.
output return loss of a 2-port with an R0
termination on the opposite port.
14
WHAT TO EXPECT
Ideal Lossless T-line
T
Ed
Zo, Hr
Ideal “X” dB Attenuator
PAD
Ideal “G” dB Gain Amp
S11=S22=0
S21=S12=1e-jT
S21DB=0
S11=S22=0
S21=S12=xe-jTpad
S21DB= X=20log(|S21|)
x =10-X/20
S11 = S22 = 0 = S12
S21 = gve-jTamp
S21DB= G=20log(S21)
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gv
G
10 20
15
WHAT TO EXPECT: Ideal Filters
Ideal Band Pass
S21
Ideal Low Pass
S21
fc1
fc2
Ideal High Pass
0dB
S21
fc
fc
GENERAL “IN-BAND”
GENERAL “OUT-OF-BAND”
S11=S22=0
S21=S12=1e-jTf)
S21(dB)=S12(dB)=0dB
|S11|=|S22|=1
S21=S12=0
S11(dB)=S22(dB)=0dB
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